Gail Roberts, More Able and Talented Coordinator at Llanfoist Fawr Primary School, shares a simple but effective activity to engage and challenge all learners – combining mathematics, oracy, collaborative working and more…

Facilitating learning, rather than directional teaching, not only ensures children take ownership, it also opens the floodgates to more able learners. Obviously it is vital to choose an effective challenging task and teach the skills they need beforehand, in order for learners to access the experience fully and develop it further through ongoing evaluation.
 
In the past at school, children may have brought cakes in from home to sell as an enterprise activity. Although this is usually an enjoyable experience, it isn’t a true representation of the profit and loss of running a business, and fails to optimise on additional opportunities for learning.
 
In this alternative activity, I ask learners to work in teams to make 3D shapes and then come up with a plan to sell them. This gives them a tangible experience, a determination for gaining information about shapes, and a chance to make choices which they can then witness the effects of at first-hand.

Develop key skills and understanding

From two weeks before the planned “sale day”, I encourage learners to consider the skills they will need and provide opportunities for them to develop these. Identified skills include:

• Persuasive language – learners are challenged to think of sentences that will entice people to stop at their stall, come up with a catchy jingle or slogan, etc.
• Negotiation – bartering on prices for the shapes.
• Understand profit and loss and interest.
• How to keep a record of the accounts, on paper or electronically.
• Elect leaders of the group and allocate team members.
• Sell using at least two languages.
• Working effectively as a team toward a shared aim.

Teaching the children how to formulate the boxes on a spreadsheet is easy, if you have previously taught coordinates. When spoken about in simple terms, profit and loss can be seen by every child. Allowing more able learners to formulate the spreadsheet gives them the opportunity to make it as complex as they want, while the opportunity to develop a business plan allows more able business minds to shine.
 
Giving learners time to think and plan for the sale day ensures that ideas can be evaluated and developed, and allows the group to come together as a team.

Replicate real-life challenges

The activity can also be used to help learners develop their understanding of real-life business processes and challenges, including:

• Premises to rent – every 15 minutes learners must pay rent for their stall; if late, they incur a fine.
• Property maintenance – fines incurred for untidy stalls.  
• Marketing – stalls decorated to attract customers.
• Interest rates – opportunity to start business with a loan, which must be paid back with interest.

Allow learners to shape the activity

The learning can be further enriched by inviting learners to suggest rules for the running of the activity. For example:

• When buying, be willing to pay more if learners can answer questions on the properties and names of the shapes, and if well-made or decorated.
• If someone in the group is not working efficiently, allow the team leader to give a warning or sanction.

Over many years of facilitating this kind of learning, the outcome has never been the same twice. Learners think of things that I would never have come up with. For example, this year they discussed ideas to test individual skills and allocate jobs based on ability, rather than simply getting every team member to cut, decorate, stick and sell. They discussed ideas about firing those who weren’t working hard enough, buying other teams’ products and selling them on at a profit, buying another table to expand their company, and researching language patterns and properties of shapes in order to sell to a broader audience knowledgeably.

What learners say…

While the summary above is hopefully sufficient to allow you to run a similar activity in your school, the impact is best expressed in the words of learners themselves:
 
“I thought this was an excellent idea for learning. Without realising it, we were making many cross-curriculum links, especially between maths and oracy. We were using strategies for problem solving and working as a team. We were having fun but learning at the same time.”
 
“I think learning in this way makes it easier to learn, because we are learning important things, but at the same time having fun. I prefer learning this way. I like being in charge of my own learning, thinking outside of the box, rather than being told.”
 
“This was a fun, challenging and exciting learning environment. This made it easier to remember the skills we needed and to use them effectively.”
 
“At the start of the challenge I didn’t have a clue what a spreadsheet was, but I enjoyed the challenge and felt proud that I could format the whole sheet myself and code new boxes when I needed to.”
 
“Communicating in a different language was challenging. However, it helped me to appreciate other people’s struggles to speak English. Our group worked cooperatively, making the most of individual talents.”
 
“It didn’t feel like we were learning. However, reflecting back on what we did, I realise I learnt and used a vast range of new skills.”
 
“It took me a matter of minutes to learn the properties and names of a massive amount of different 3D shapes. This was because I had a real purpose to learn. I was so proud when a visitor asked me questions on the properties and I blew him away with my knowledge and how confidently I was able to answer his questions.” 
 
“It helped me to understand the importance of working as a team. We all had a job to do. These were selected, because we could do that particular thing really well. It made me feel like it was an actual place of work and we were actually doing a ‘job’. Real-life situations like these help me to realise the importance of everyone’s unique abilities.” 

Gail Roberts is the MAT Coordinator, Maths Coordinator and Year 5 teacher at Llanfoist Fawr Primary School in Monmouthshire. She has worked in education since 1980, starting out as an NNEB with children with severe difficulties in basic life skills, and gaining her NPQH in 2007. Llanfoist Fawr gained the NACE Challenge Award in 2017, in recognition of school-wide commitment to high-quality provision for MAT learners within a context of challenge for all.

Published earlier this term (exclusively available to NACE members), the NACE Essentials guide to realising the potential of more able learners in GCSE science offers guidance for science leaders and teachers seeking to improve the quality of challenge in their lessons. In this excerpt, guide author Ed Walsh shares 10 “killer questions” all science departments should consider when reviewing provision for those capable of attaining the highest grades in the subject.

1. How close is the relationship between objectives and questions used in lessons and the outcomes and command words used in the exam specifications?

If the former are dominated by stems such as “know” and “understand”, how well will learners be prepared to answer higher-order exam questions with stems such as “suggest” and “justify”?

2. How are learners being encouraged to apply ideas to novel contexts?

It isn’t necessarily the case that topics should start with concepts and then progress to application; in some cases, application may be a good way to introduce a topic and develop ideas.

3. Are learners presented with evidence to analyse?

What opportunities do they have to engage with something such as a diagram or graph to make sense of and interpret? 

4. What common cause is being made with maths?

What might be learned if a science teacher were to observe more able learners being taught maths, and the maths teacher then to see them in science?

5. Are maths skills being ramped up?

It’s worth deconstructing stretch and challenge questions in terms of the maths skills and then thinking through how to teach these. As well as having mastery of individual skills, students need to be able to select and combine skills.

6. Is a good range of types of high-level questions being used?

Make sure these are not solely based on understanding complex ideas. When asking higher-level questions you can increase challenge by altering the stem of the question, broadening the range of command words you use. You can also ask for a longer response, possibly one that requires linking ideas from different parts of the subject.

7. Is the teacher modelling effective practice in answering extended questions?

Can students recognise such a question, and plan a structure and approach to answering it? Try modelling the construction of a high-quality response, showing how you select key terms, structure the writing and ensure it matches what the examiner is looking for.

8. How effectively is assessment data being used to identify development areas?

How well can learners complete the sentence “To get a good result in science I need to focus on…”? What’s guiding their revision?

9. How has data from the summer 2018 series been used to identify development areas?

It should be possible to interrogate candidate performance to answer questions such as “How well did high-attaining learners in my school cope with AO2 questions and how does this compare with the national picture?”

10. How well does KS3 prepare students for GCSE science?

Is the KS3 course doing its job in terms of getting more able learners to be “GCSE-ready”? How well does it support able learners to master key ideas, understand how to investigate various phenomena and use skills from other parts of the curriculum such as working numerically and developing written responses?

Read more…

• Log in to our members’ site for the full NACE Essentials guide to realising the potential of more able learners in GCSE science. 
• Not yet a member? Find out more.

1. Offer a challenging task related to the class activity.

2. Tailor homework to the learner’s interests.

3. Consider setting work usually covered later in the key stage.

4. Have a long-term plan for the learner's mathematical education.

5. Support the learner's interest in mathematics outside school.

There are lots of opportunities for exceptionally able learners to pursue their interest in mathematics outside of school, and to meet peers with similar interests and abilities. Keep an eye on opportunities provided by the UK Mathematics Trust (UKMT) and the Royal Institution Masterclass series, for example. The UKMT also offers a free mentoring service, providing mentors to help young mathematicians develop their problem-solving skills.

More free resources from NRICH:

• Be a Mathematician! (for primary learners)
• Thinking Mathematically (secondary)
• Recommended books (primary)
• Recommended books (secondary)

Lesley Hill, headteacher of NACE member Lavender Primary School in North London, explains how the school’s approach to marking and feedback has evolved alongside the development of a strong learning mindset culture.

Our marking and feedback policy cannot stand alone. It only works because we have embedded the learning culture on which it depends.

About five years ago, we were proudly using assessment for learning (AfL) strategies, such as no hands up, colourful cups, and thumbs up, thumbs down and thumbs somewhere in between. None of this was particularly useful for those learners who were unable to be honest about where they were in their understanding. This became apparent to me during a Year 2 literacy lesson. I shook my lolly-stick pot and was ready to pick a child to answer my question, when a higher achiever visibly shuddered. That said it all.

We turned to the work of Carol Dweck and immediately introduced growth mindset, understanding that higher-achieving children can often be those with the most fixed mindsets, causing barriers to learning.

Developing skills for effective learning

We knew that embedding a growth mindset culture was essential, but we also realised very quickly that the skills of being a good learner had to be taught too. A school full of determined children chanting (albeit sweetly) “We can do it!” doesn’t necessarily mean better outcomes. We introduced themes around Guy Claxton’s work, Learning to Learn, and our children learnt to be resourceful and reflective, as well as resilient.

We also understood that if children were truly going to understand where they were as learners, we needed to examine our success criteria. Hours had been spent trying to put English success criteria into a hierarchical order with a must, a should and a could. Whilst our lower-achieving children stayed safely with the “musts”, some of the higher-achievers completed the “should” and “coulds” and missed some basic “musts” altogether. We ditched MSC for toolkits, after attending a Pie Corbett course.

Giving children ownership of their learning

The same training also prompted us to establish cooperative reviews, which offer a focused and structured peer assessment strategy. We have trained our children to give effective feedback and to have useful discussions around their learning. This is key. Our current marking policy includes lots of peer assessment and reflection, which begins to give ownership to the child. We firmly believe that ownership of learning impacts positively on children’s motivation to challenge themselves.

This ownership was previously promoted by allowing learners to choose their own level of maths tasks, where they would be encouraged to make decisions about the levels of challenge they could manage. We have since bought a Singapore Maths scheme; the reflective approach and decisions around which strategy to use to solve a problem fit perfectly with challenge and ownership.

Learners also have ownership over the marking of maths. The answers are on the tables and learners check after solving a few problems. If they have some wrong, they will unpick the steps they have gone through to understand where they have made an error or have a misconception. This deeper-level thinking can enable them to change their approach to get a solution. Should they not be able to see where they have gone wrong, the teacher will step in to guide or re-teach through a face-to-face conference.

Moving on from written marking

Conferences have taken the place of written marking. It was apparent to us for some time that reams of written marking or rows of ticks and dots, carried out away from the learning context and delivered back the next day, was, at best, hard for children to relate to and, at worst, a meaningless waste of time. With teacher workload high on the agenda, our decision to stop written marking altogether, for every subject, was not difficult to make. Our children already owned their learning, they knew how to self- and peer-assess effectively, and they were reflective, resilient and skilled learners. It was an easy step to hand over the pen.

Our marking and feedback procedure is simple. Children mark their own work according to the success criteria and they write a reflection on their learning – commenting on their understanding, successes and difficulties. They are also challenged to consider how they have approached the work and what they might do differently. Teachers look at the books every day and identify where there is a need to support or extend children’s learning. They plan in targeted 1:1 or group conferences for the following day, or hold spontaneous conferences, to address misconceptions, clarify points and extend thinking. During conference discussions, children are encouraged to consider where they have met their targets and to choose new ones, and to talk about the reflections they have made.

Children’s reflections are a window to their understanding, not just of concepts, but of themselves as learners. They provide teachers with far greater insight than a piece of work on its own and thus teachers can cater far more effectively for each child’s needs. Our approach to marking is not a stand-alone. It is an extension to the learning culture we have worked to create: a culture of learners who can recognise and be honest about where they are, who know where they need to go, and who are not afraid to share the responsibility for getting there.

Lesley Hill is headteacher of Lavender Primary School, a popular two-form entry school in North London, part of the Ivy Learning Trust and a member of NACE. She has taught across the primary age range and has also worked in adult basic education and on teacher training programmes. Her current role includes the design and delivery of leadership training at middle and senior leader level, and she also provides workshops on a range of subjects, such as growth mindset and marking. Her forthcoming book, Once Upon a Green Pen, explores approaches to create the right school culture.

Read more: log in to our members’ area to access the NACE Essentials guide to learning mindset, and the accompanying webinar.

NACE is proud to partner with the NRICH project at the University of Cambridge’s Centre for Mathematical Sciences, which offers free online resources to enrich the mathematics curriculum, provide challenging and meaningful activities, and develop mathematical thinking and problem-solving skills. In this blog post, the project’s director, Ems Lord, explains why and how NRICH is developing resources designed to get GCSE students seriously interested in Further Mathematics…

Entries for the Further Mathematics A-level have tripled in recent years, from around 5,000 students in 2005 to a staggering 15,000 by 2015 (source: JCQ). But one of the greatest recent success stories in mathematics is under threat.


Figure 1: Entries for Further Mathematics up to 2016 (source: JCQ)

The transformation of Further Mathematics has all the ingredients of a great news story, yet the latest figures are alarming. Anecdotal evidence from both schools and colleges indicate a staggering 50% drop in the number of students opting to study Further Mathematics this year.

Recent changes in national policy promoting the study of three A-levels have hit Further Mathematics – often regarded as a fourth option – harder than most subjects. The NRICH team at the University of Cambridge has joined up with colleagues at the University of Oxford to address concerns regarding the current decline in Further Mathematics entries. The realisation that many GCSE students do not appreciate the opportunities offered by Further Mathematics led to our new set of free resources for schools, which we’ve called Adventures with Complex Numbers.

Why focus on complex numbers?

What resources are available?

So, they’re interested… What next?